A002668 Continued cotangent for e. (Formerly M1900 N0748)

2, 8, 75, 8949, 119646723, 15849841722437093, 708657580163382065836292133774995, 529026553215766321676623343348414600292754204772300344704877695232

Offset

1,1

References

D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Harry J. Smith, Table of n, a(n) for n = 1..11

D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340. [Annotated scanned copy]

Eric Weisstein's World of Mathematics, Lehmer Cotangent Expansion

Mathematica

b[1] = E; b[n_] := b[n] = (b[n-1]*Floor[b[n-1]]+1) / (b[n-1]-Floor[b[n-1]]); a[n_] := Floor[b[n]]; Table[a[n], {n, 1, 8}] (* Jean-François Alcover, Jan 17 2012, after PARI *)

Prog

(PARI) { default(realprecision, 10000); bn=vector(11); bn[1]=exp(1); for(n=2, 11, bn[n]=(bn[n-1]*floor(bn[n-1]) + 1)/(bn[n-1] - floor(bn[n-1]))); for (n=1, 11, write("b002668.txt", n, " ", floor(bn[n]))); } \\ Harry J. Smith, May 04 2009

Crossrefs

Sequence in context: A356746 A132039 A204552 * A193205 A303943 A295345

Adjacent sequences: A002665 A002666 A002667 * A002669 A002670 A002671

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Jeffrey Shallit

Status

approved